Such a high-pressure discharge lamp is described, for example, in the laid-open specification EP 1 465 237 A2. The mercury-free, ionizable fill of the high-pressure discharge lamp disclosed in EP 1 465 237 A2 contains zinc iodide and indium iodide, wherein the weight ratio of zinc iodide and indium iodide is 12.5. The coldfilling pressure of the xenon is 1.18 megapascal and the discharge vessel has a volume of 24 mm3. The high-pressure discharge lamp is used as a light source in a vehicle headlight.